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<H3>fix ave/spatial command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID ave/spatial Nevery Nrepeat Nfreq dim origin delta ... value1 value2 ... keyword args ... 
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command 

<LI>ave/spatial = style name of this fix command 

<LI>Nevery = use input values every this many timesteps 

<LI>Nrepeat = # of times to use input values for calculating averages 

<LI>Nfreq = calculate averages every this many timesteps 

<LI>dim, origin, delta can be repeated 1, 2, or 3 times for 1d, 2d, or 3d bins 

<PRE>  dim = <I>x</I> or <I>y</I> or <I>z</I>
  origin = <I>lower</I> or <I>center</I> or <I>upper</I> or coordinate value (distance units)
  delta = thickness of spatial bins in dim (distance units) 
</PRE>
<LI>one or more input values can be listed 

<LI>value = vx, vy, vz, fx, fy, fz, density/mass, density/number, c_ID, c_ID[I], f_ID, f_ID[I], v_name 

<PRE>  vx,vy,vz,fx,fy,fz = atom attribute (velocity, force component)
  density/number, density/mass = number or mass density
  c_ID = per-atom vector calculated by a compute with ID
  c_ID[I] = Ith column of per-atom array calculated by a compute with ID
  f_ID = per-atom vector calculated by a fix with ID
  f_ID[I] = Ith column of per-atom array calculated by a fix with ID
  v_name = per-atom vector calculated by an atom-style variable with name 
</PRE>
<LI>zero or more keyword/arg pairs may be appended 

<LI>keyword = <I>norm</I> or <I>units</I> or <I>file</I> or <I>ave</I> or <I>overwrite</I> or <I>title1</I> or <I>title2</I> or <I>title3</I> 

<PRE>  <I>units</I> arg = <I>box</I> or <I>lattice</I> or <I>reduced</I>
  <I>norm</I> arg = <I>all</I> or <I>sample</I>
  <I>region</I> arg = region-ID
    region-ID = ID of region atoms must be in to contribute to spatial averaging
  <I>ave</I> args = <I>one</I> or <I>running</I> or <I>window M</I>
    one = output new average value every Nfreq steps
    running = output cumulative average of all previous Nfreq steps
    window M = output average of M most recent Nfreq steps
  <I>file</I> arg = filename
    filename = file to write results to
  <I>overwrite</I> arg = none = overwrite output file with only latest output
  <I>title1</I> arg = string
    string = text to print as 1st line of output file
  <I>title2</I> arg = string
    string = text to print as 2nd line of output file
  <I>title3</I> arg = string
    string = text to print as 3rd line of output file 
</PRE>

</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all ave/spatial 10000 1 10000 z lower 0.02 c_myCentro units reduced &
                      title1 "My output values"
fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 vx vz norm sample file vel.profile
fix 1 flow ave/spatial 100 5 1000 z lower 1.0 y 0.0 2.5 density/mass ave running 
</PRE>
<P><B>Description:</B>
</P>
<P>Use one or more per-atom vectors as inputs every few timesteps, bin
their values spatially into 1d, 2d, or 3d bins based on current atom
coordinates, and average the bin values over longer timescales.  The
resulting bin averages can be used by other <A HREF = "Section_howto.html#howto_15">output
commands</A> such as <A HREF = "thermo_style.html">thermo_style
custom</A>, and can also be written to a file.
</P>
<P>The group specified with the command means only atoms within the group
contribute to bin averages.  If the <I>region</I> keyword is used, the
atom must be in both the group and the specified geometric
<A HREF = "region.html">region</A> in order to contribute to bin averages.
</P>
<P>Each listed value can be an atom attribute (position, velocity, force
component), a mass or number density, or the result of a
<A HREF = "compute.html">compute</A> or <A HREF = "fix.html">fix</A> or the evaluation of an
atom-style <A HREF = "variable.html">variable</A>.  In the latter cases, the
compute, fix, or variable must produce a per-atom quantity, not a
global quantity.  If you wish to time-average global quantities from a
compute, fix, or variable, then see the <A HREF = "fix_ave_time.html">fix
ave/time</A> command.
</P>
<P><A HREF = "compute.html">Computes</A> that produce per-atom quantities are those
which have the word <I>atom</I> in their style name.  See the doc pages for
individual <A HREF = "fix.html">fixes</A> to determine which ones produce per-atom
quantities.  <A HREF = "variable.html">Variables</A> of style <I>atom</I> are the only
ones that can be used with this fix since all other styles of variable
produce global quantities.
</P>
<P>The per-atom values of each input vector are binned and averaged
independently of the per-atom values in other input vectors.
</P>
<P>The size and dimensionality of the bins (1d = layers or slabs, 2d =
pencils, 3d = boxes) are determined by the <I>dim</I>, <I>origin</I>, and
<I>delta</I> settings and how many times they are specified (1, 2, or 3).
See details below.
</P>
<P>IMPORTANT NOTE: This fix works by creating an array of size Nbins by
Nvalues on each processor.  Nbins is the total number of bins; Nvalues
is the number of input values specified.  Each processor loops over
its atoms, tallying its values to the appropriate bin.  Then the
entire array is summed across all processors.  This means that using a
large number of bins (easy to do for 2d or 3d bins) will incur an
overhead in memory and computational cost (summing across processors),
so be careful to use reasonable numbers of bins.
</P>
<HR>

<P>The <I>Nevery</I>, <I>Nrepeat</I>, and <I>Nfreq</I> arguments specify on what
timesteps the input values will be used to bin them and contribute to
the average.  The final averaged quantities are generated on timesteps
that are a multiples of <I>Nfreq</I>.  The average is over <I>Nrepeat</I>
quantities, computed in the preceding portion of the simulation every
<I>Nevery</I> timesteps.  <I>Nfreq</I> must be a multiple of <I>Nevery</I> and
<I>Nevery</I> must be non-zero even if <I>Nrepeat</I> is 1.  Also, the timesteps
contributing to the average value cannot overlap, i.e. Nfreq >
(Nrepeat-1)*Nevery is required.
</P>
<P>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on
timesteps 90,92,94,96,98,100 will be used to compute the final average
on timestep 100.  Similarly for timesteps 190,192,194,196,198,200 on
timestep 200, etc.  If Nrepeat=1 and Nfreq = 100, then no time
averaging is done; values are simply generated on timesteps
100,200,etc.
</P>
<HR>

<P>Each per-atom property is also averaged over atoms in each bin.  Bins
can be 1d layers or slabs, 2d pencils, or 3d boxes.  This depends on
how many times (1, 2, or 3) the <I>dim</I>, <I>origin</I>, and <I>delta</I> settings
are specified in the fix ave/spatial command.  For 2d or 3d bins,
there is no restriction on specifying dim = x before dim = y, or dim =
y before dim = z.  Bins in a particular <I>dim</I> have a bin size in that
dimension given by <I>delta</I>.  Every Nfreq steps, when averaging is
being performed and the per-atom property is calculated for the first
time, the number of bins and the bin sizes and boundaries are
computed.  Thus if the simulation box changes size during a
simulation, the number of bins and their boundaries may also change.
In each dimension, bins are defined relative to a specified <I>origin</I>,
which may be the lower/upper edge of the simulation box (in <I>dim</I>) or
its center point, or a specified coordinate value.  Starting at the
origin, sufficient bins are created in both directions to completely
cover the box.  On subsequent timesteps every atom is mapped to one of
the bins.  Atoms beyond the lowermost/uppermost bin in a dimension are
counted in the first/last bin in that dimension.
</P>
<P>For orthogonal simulation boxes, the bins are also layers, pencils, or
boxes aligned with the xyz coordinate axes.  For triclinic
(non-orthogonal) simulation boxes, the bins are so that they are
parallel to the tilted faces of the simulation box.  See <A HREF = "Section_howto.html#howto_12">this
section</A> of the manual for a discussion of
the geometry of triclinic boxes in LAMMPS.  As described there, a
tilted simulation box has edge vectors a,b,c.  In that nomenclature,
bins in the x dimension have faces with normals in the "b" cross "c"
direction.  Bins in y have faces normal to the "a" cross "c"
direction.  And bins in z have faces normal to the "a" cross "b"
direction.  Note that in order to define the size and position of
these bins in an unambiguous fashion, the <I>units</I> option must be set
to <I>reduced</I> when using a triclinic simulation box, as noted below.
</P>
<HR>

<P>The atom attribute values (vx,vy,vz,fx,fy,fz) are self-explanatory.
Note that other atom attributes (including atom postitions x,y,z) can
be used as inputs to this fix by using the <A HREF = "compute_property_atom.html">compute
property/atom</A> command and then specifying
an input value from that compute.
</P>
<P>The <I>density/number</I> value means the number density is computed in
each bin, i.e. a weighting of 1 for each atom.  The <I>density/mass</I>
value means the mass density is computed in each bind, i.e. each atom
is weighted by its mass.  The resulting density is normalized by the
volume of the bin so that units of number/volume or density are
output.  See the <A HREF = "units.html">units</A> command doc page for the
definition of density for each choice of units, e.g. gram/cm^3.
</P>
<P>If a value begins with "c_", a compute ID must follow which has been
previously defined in the input script.  If no bracketed integer is
appended, the per-atom vector calculated by the compute is used.  If a
bracketed integer is appended, the Ith column of the per-atom array
calculated by the compute is used.  Users can also write code for
their own compute styles and <A HREF = "Section_modify.html">add them to LAMMPS</A>.
</P>
<P>If a value begins with "f_", a fix ID must follow which has been
previously defined in the input script.  If no bracketed integer is
appended, the per-atom vector calculated by the fix is used.  If a
bracketed integer is appended, the Ith column of the per-atom array
calculated by the fix is used.  Note that some fixes only produce
their values on certain timesteps, which must be compatible with
<I>Nevery</I>, else an error results.  Users can also write code for their
own fix styles and <A HREF = "Section_modify.html">add them to LAMMPS</A>.
</P>
<P>If a value begins with "v_", a variable name must follow which has
been previously defined in the input script.  Variables of style
<I>atom</I> can reference thermodynamic keywords and various per-atom
attributes, or invoke other computes, fixes, or variables when they
are evaluated, so this is a very general means of generating per-atom
quantities to spatially average.
</P>
<HR>

<P>Additional optional keywords also affect the operation of this fix.
</P>
<P>The <I>units</I> keyword determines the meaning of the distance units used
for the bin size <I>delta</I> and for <I>origin</I> if it is a coordinate
value.  For orthogonal simulation boxes, any of the 3 options may be
used.  For non-orthogonal (triclinic) simulation boxes, only the
<I>reduced</I> option may be used.
</P>
<P>A <I>box</I> value selects standard distance units as defined by the
<A HREF = "units.html">units</A> command, e.g. Angstroms for units = real or metal.
A <I>lattice</I> value means the distance units are in lattice spacings.
The <A HREF = "lattice.html">lattice</A> command must have been previously used to
define the lattice spacing.  A <I>reduced</I> value means normalized
unitless values between 0 and 1, which represent the lower and upper
faces of the simulation box respectively.  Thus an <I>origin</I> value of
0.5 means the center of the box in any dimension.  A <I>delta</I> value of
0.1 means 10 bins span the box in that dimension.
</P>
<P>Consider a non-orthogonal box, with bins that are 1d layers or slabs
in the x dimension.  No matter how the box is tilted, an <I>origin</I> of
0.0 means start layers at the lower "b" cross "c" plane of the
simulation box and an <I>origin</I> of 1.0 means to start layers at the
upper "b" cross "c" face of the box.  A <I>delta</I> value of 0.1 means
there will be 10 layers from 0.0 to 1.0, regardless of the current
size or shape of the simulation box.
</P>
<P>The <I>norm</I> keyword affects how averaging is done for the output
produced every <I>Nfreq</I> timesteps.  For an <I>all</I> setting, a bin
quantity is summed over all atoms in all <I>Nrepeat</I> samples, as is the
count of atoms in the bin.  The printed value for the bin is
Total-quantity / Total-count.  In other words it is an average over
the entire <I>Nfreq</I> timescale.
</P>
<P>For a <I>sample</I> setting, the bin quantity is summed over atoms for only
a single sample, as is the count, and a "average sample value" is
computed, i.e. Sample-quantity / Sample-count.  The printed value for
the bin is the average of the <I>Nrepeat</I> "average sample values", In
other words it is an average of an average.
</P>
<P>The <I>ave</I> keyword determines how the bin values produced every <I>Nfreq</I>
steps are averaged with bin values produced on previous steps that
were multiples of <I>Nfreq</I>, before they are accessed by another output
command or written to a file.
</P>
<P>If the <I>ave</I> setting is <I>one</I>, then the bin values produced on
timesteps that are multiples of <I>Nfreq</I> are independent of each other;
they are output as-is without further averaging.
</P>
<P>If the <I>ave</I> setting is <I>running</I>, then the bin values produced on
timesteps that are multiples of <I>Nfreq</I> are summed and averaged in a
cumulative sense before being output.  Each output bin value is thus
the average of the bin value produced on that timestep with all
preceding values for the same bin.  This running average begins when
the fix is defined; it can only be restarted by deleting the fix via
the <A HREF = "unfix.html">unfix</A> command, or re-defining the fix by
re-specifying it.
</P>
<P>If the <I>ave</I> setting is <I>window</I>, then the bin values produced on
timesteps that are multiples of <I>Nfreq</I> are summed and averaged within
a moving "window" of time, so that the last M values for the same bin
are used to produce the output.  E.g. if M = 3 and Nfreq = 1000, then
the output on step 10000 will be the average of the individual bin
values on steps 8000,9000,10000.  Outputs on early steps will average
over less than M values if they are not available.
</P>
<P>The <I>file</I> keyword allows a filename to be specified.  Every <I>Nfreq</I>
timesteps, a section of bin info will be written to a text file in the
following format.  A line with the timestep and number of bin is
written.  Then one line per bin is written, containing the bin ID
(1-N), the coordinate of the center of the bin, the number of atoms
in the bin, and one or more calculated values.  The number of values
in each line corresponds to the number of values specified in the fix
ave/spatial command.  The number of atoms and the value(s) are average
quantities.  If the value of the <I>units</I> keyword is <I>box</I> or
<I>lattice</I>, the "coord" is printed in box units.  If the value of the
<I>units</I> keyword is <I>reduced</I>, the "coord" is printed in reduced units
(0-1).
</P>
<P>The <I>overwrite</I> keyword will continuously overwrite the output file
with the latest output, so that it only contains one timestep worth of
output.  This option can only be used with the <I>ave running</I> setting.
</P>
<P>The <I>title1</I> and <I>title2</I> and <I>title3</I> keywords allow specification of
the strings that will be printed as the first 3 lines of the output
file, assuming the <I>file</I> keyword was used.  LAMMPS uses default
values for each of these, so they do not need to be specified.
</P>
<P>By default, these header lines are as follows:
</P>
<PRE># Spatial-averaged data for fix ID and group name
# Timestep Number-of-bins
# Bin Coord1 Coord2 Coord3 Count value1 value2 ... 
</PRE>
<P>In the first line, ID and name are replaced with the fix-ID and group
name.  The second line describes the two values that are printed at
the first of each section of output.  In the third line the values are
replaced with the appropriate fields from the fix ave/spatial command.
The Coord2 and Coord3 entries in the third line only appear for 2d and
3d bins respectively.  For 1d bins, the word Coord1 is replaced by
just Coord.
</P>
<HR>

<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>.  None of the <A HREF = "fix_modify.html">fix_modify</A> options
are relevant to this fix.
</P>
<P>This fix computes a global array of values which can be accessed by
various <A HREF = "Section_howto.html#howto_15">output commands</A>.  The values can
only be accessed on timesteps that are multiples of <I>Nfreq</I> since that
is when averaging is performed.  The global array has # of rows =
Nbins and # of columns = Ndim+1+Nvalues, where Ndim = 1,2,3 for
1d,2d,3d bins.  The first 1 or 2 or 3 columns have the bin coordinates
(center of the bin) in the appropriate dimensions, the next column has
the count of atoms in that bin, and the remaining columns are the
Nvalue quantities.  When the array is accessed with an I that exceeds
the current number of bins, than a 0.0 is returned by the fix instead
of an error, since the number of bins can vary as a simulation runs,
depending on the simulation box size.  2d or 3d bins are ordered so
that the last dimension(s) vary fastest.  The array values calculated
by this fix are "intensive", since they are already normalized by the
count of atoms in each bin.
</P>
<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
the <A HREF = "run.html">run</A> command.  This fix is not invoked during <A HREF = "minimize.html">energy
minimization</A>.
</P>
<P><B>Restrictions:</B>
</P>
<P>When the <I>ave</I> keyword is set to <I>running</I> or <I>window</I> then the number
of bins must remain the same during the simulation, so that the
appropriate averaging can be done.  This will be the case if the
simulation box size doesn't change or if the <I>units</I> keyword is set to
<I>reduced</I>.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "compute.html">compute</A>, <A HREF = "fix_ave_atom.html">fix ave/atom</A>, <A HREF = "fix_ave_histo.html">fix
ave/histo</A>, <A HREF = "fix_ave_time.html">fix ave/time</A>,
<A HREF = "variable.html">variable</A>, <A HREF = "fix_ave_correlate.html">fix ave/correlate</A>,
</P>
<P><B>Default:</B>
</P>
<P>The option defaults are units = lattice, norm = all, no file output,
and ave = one, title 1,2,3 = strings as described above.
</P>
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